Generalized Thermoelasticity Theory Research Articles

Analysis of the magnetic-thermal response of viscoelastic rotating nanobeams based on nonlocal theory and memory effect

Size-dependent effects in elastic deformation and thermal hysteresis effects in the heat transfer process are significant for small-size structures or devices. As an important component of micro- and nanoelectromechanical systems, the analysis of the thermodynamic properties of rotating nanobeams is crucial for the safe operation of the system. This work aims to construct a new nonlocal thermo-viscoelastic model and use this model to analyze the thermodynamic behavior of rotating nanobeams at the microscale. In this work, fractional order Kelvin-Voigt theory describes the viscoelasticity of materials. Moreover, the theory of continuous medium mechanics is improved by introducing nonlocal parameters to capture the size effect during deformation. Based on the generalized thermoelasticity theory, memory-dependent derivatives predict hysteresis effects during heat transfer. Nanobeams are placed in a longitudinal magnetic field. Graphene strips connected to a power supply are used as the nanobeam heat source. The effects of nonlocal parameters, damping coefficients, and fractional order parameters on the dynamic response of the system are analyzed. In addition, a new comparative study of the effects of voltage and resistance on the system is made in the context of the nonlocal generalized thermoelasticity theory.

Fractional-order strain of an infinite annular cylinder based on Caputo and Caputo–Fabrizio fractional derivatives under hyperbolic two-temperature generalized thermoelasticity theory

Fractional-order strain of an infinite annular cylinder based on Caputo and Caputo–Fabrizio fractional derivatives under hyperbolic two-temperature generalized thermoelasticity theory

Some qualitative results in hyperbolic two-temperature generalized thermoelasticity

This study aims to establish the convolutional-type variational and reciprocity theorems within the framework of the hyperbolic two-temperature generalized thermoelasticity theory for an isotropic thermoelastic material, with the help of alternate formulation of the mixed boundary initial value problem, in which initial conditions are combined with field equations (using the Laplace transform). The convolutional-type variational principle adapts readily to numerical solutions based on the Ritz method and is useful in the finite element method. The reciprocity theorem is helpful in the theoretical development of boundary and finite element methods. The current effort can be valuable for the problem of coupling effects of thermal and mechanical fields, especially in geophysics and mining.

Photo-thermo-elastic interactions in micropolar generalized thermoelasticity theory in the framework of Green-Naghdi theory

The purpose of the current study is to establish a novel mathematical model in the micropolar theory of generalized thermoelasticity under the framework of photothermal theory. For the solution of the required problem, the integral transforms along with the potential displacement approach has been utilized. For graphical representation of different physical quantities such as displacement components, force and couple stress components, carrier density as well as the temperature distribution, Matlab software has been used.

Non-Fourier thermoelastic damping in small-sized ring resonators with circular cross section according to Moore–Gibson–Thompson generalized thermoelasticity theory

Non-Fourier thermoelastic damping in small-sized ring resonators with circular cross section according to Moore–Gibson–Thompson generalized thermoelasticity theory

Nonlocal dual-phase-lag thermoelastic damping in small-sized circular cross-sectional ring resonators

The purpose of current research is to establish a theoretical size-dependent framework for estimating the amount of thermoelastic damping (TED) in miniaturized rings with circular cross section via the nonlocal dual-phase-lag (NDPL) generalized thermoelasticity theory, as one of the most exhaustive non-Fourier heat conduction models. The method used to achieve this goal is based on the definition of TED in the energy dissipation (ED) approach. To do so, after deriving heat equation in the context of NDPL model, the distribution of temperature all over the volume of the ring is specified. Then, the relations of dissipated thermal energy and strain energy in the ring are obtained. Lastly, by employing ED approach, a formula comprising the nonclassical parameters of NDPL model is rendered to determine TED value in small-scaled toroidal rings. By presenting various numerical examples, the dependence of TED on influential parameters including nonclassical thermal constants in NDPL model, ring geometry, vibrational mode number and ring material is surveyed. The Findings enlighten that the inclusion of nonlocal parameter into the model can have conspicuous impacts on TED value, especially in smaller rings or higher vibrational mode numbers. The results also reveal that among the investigated materials (i.e. silicon, copper, silver, and lead), rings made of lead and silicon exhibit the maximum and minimum TED values, respectively.

Effect of magnetic field on a thermoviscoelastic body via a refined two-temperature Lord–Shulman model

This paper aims to modify the generalized thermoelasticity theory of Lord–Shulman. Higher-order time-derivative terms are incorporated to get accurate field variables. The refined theory is employed to examine the inclusion of a magnetic field, a two-temperature parameter, and the viscoelastic effects on a thermoelastic medium with two temperatures. The problem has been solved analytically and numerical data have been obtained by utilizing the normal mode technique. The analytic expressions of the displacements, stresses, dilatation, thermodynamic and conductive temperatures are outlined and investigated. The outcomes are reported for future comparison, and some are presented graphically in 2D and 3D plots. Comparisons with the existing literature due to the classical coupled and simple Lord–Shulman thermoviscoelasticity theories are made. The effects of many parameters are discussed.

General generalized thermoelasticity theory (GGTT)

General generalized thermoelasticity theory (GGTT)

Refined Dual-Phase-Lag Theory for the 1D Behavior of Skin Tissue under Ramp-Type Heating

In this article, a mathematical analysis of thermoelastic skin tissue is presented based on a refined dual-phase-lag (DPL) thermal conduction theory that considers accounting for the effect of multiple time derivatives. The thin skin tissue is regarded as having mechanically clamped surfaces that are one-dimensional. Additionally, the skin tissue undergoes ramp-type heating on its outer surface, whereas its inner surface keeps the assessed temperature from vanishing. Some of the previous generalized thermoelasticity theories were obtained from the proposed model. The distributions of temperature, displacement, dilatation, and stress are attained by applying the Laplace transform and its numerical reversal approaches. The outcomes are explicitly illustrated to examine the significant influences on the distributions of the field variables. The refined DPL bioheat conduction model in this study predicts temperature, and the findings revealed that the model is located among the existing generalized thermoelastic theories. These findings offer a more thorough understanding of how skin tissue behaves when exposed to a particular boundary condition temperature distribution.

Refined Green–Lindsay Model for the Response of Skin Tissue under a Ramp-Type Heating

Based on Green–Lindsay generalized thermoelasticity theory, this paper presents a new refined higher-order time-derivative thermoelasticity model. Thinner one-dimensional skin tissue is considered when its inner surface is free of traction and does not show any temperature increase. The skin tissue’s bounding surface has been heated by ramp-type heating. The classical thermoelastic theories are obtained from the present general formula. The governing equations of the present model are obtained. To move the system into a space state, the Laplace transform is used. The inverse of the Laplace transform is also used with Tzuo’s method to solve the problem. As a result, the field quantities are obtained numerically, and the results of the current model are graphically represented with a comparison to two different theories of thermoelasticity. The effects of various parameters on thermomechanical waves through the skin tissue are analyzed. The theory notes a vibrational behavior in heat transfer and a different effect on the parameters discussed in this article.

Modeling the viscosity and rotation on a generalized micropolar thermoelasticity with two-temperature under five theories

ABSTRACT The current study establishes the generalized micropolar thermo-visco-elasticity model in an isotropic elastic material with two temperatures. At a uniform angular velocity, the entire elastic medium is rotated. The description is implemented under five generalized thermoelasticity theories: Lord-Shulman (L-S) with one relaxation time, Green-Lindsay (G-L) with two relaxation times, Green-Naghdi theory (G-N II) without energy dissipation, and Tzou theory with dual phase lags (DPL), much like the coupled theory. We used the normal mode analysis to obtain the specific articulations for the considering factors. Additionally, some specific cases are discussed with regard to the problem. Numerical findings are collected and displayed graphically for the variables under consideration. Different theories (L-S, G-L, G-N II, and DPL), rotation, viscosity, and two temperatures were used to predict the results.

A Size-Dependent Generalized Thermoelasticity Theory for Thermoelastic Damping in Vibrations of Nanobeam Resonators

Thermoelastic damping (TED) has been discerned as a definite source of intrinsic energy loss in miniaturized mechanical elements. The size-dependent structural and thermal behavior of these small-sized structures has been proven through experimental observations. As a first attempt, this article exploits nonlocal strain gradient theory (NSGT) and nonlocal dual-phase-lag (NDPL) heat conduction model simultaneously to acquire a mathematical formulation and analytical solution for TED in nanobeams that can accommodate size effect into both structural and heat transfer fields. For this purpose, the coupled equations of motion and heat conduction are firstly extracted via NSGT and NDPL model. Next, by deriving the distribution of temperature from heat conduction equation and substituting it in the motion equation, the unconventional thermoelastic frequency equation is established. By deriving the real and imaginary parts of the frequency from this equation and employing the definition of quality factor, an explicit solution is given for approximating TED value. The veracity of the proposed model is checked by comparing it with the solutions reported in the literature for specific and simpler cases. A diverse set of numerical results is then presented to appraise the influence of some factors like structural and thermal nonlocal parameters, strain gradient length scale parameter, geometrical parameters, mode number and material on the amount of TED. According to the results, use of NDPL model yields a smaller value for TED than DPL model, but prediction of NSGT about the magnitude of TED, in addition to the relative amounts of its two scale parameters, strongly depend on other factors such as aspect ratio, vibration mode and material type.

Plane waves in Moore–Gibson–Thompson thermoelasticity considering nonlocal elasticity effect

The Moore–Gibson–Thompson (MGT) generalized thermoelasticity theory together with the Eringen’s nonlocal elasticity model is used to study the propagation of harmonic plane waves in an infinite elastic medium that conducts heat. Two sets of coupled longitudinal thermoelastic waves have been initiated. These waves are dispersive in nature and experience attenuation. In conjunction with the coupled waves, there also exists one uncoupled vertically shear–type (SV-type) wave. The SV-type wave is dispersive in nature but without any attenuation. The elastic nonlocality parameter influences all these waves. Furthermore, the SV-type wave faces critical frequency, while the coupled longitudinal waves may face critical frequencies conditionally. We also explore the problem of reflection of thermoelastic waves at a stress-free insulated and isothermal plane boundary of the medium considered here. The reflection coefficients and their respective energy ratios of the reflected waves to that of incident wave are determined analytically and numerically by considering an appropriate material. The numerical results are presented graphically to highlight the effects of various parameters of interest. Some important observations about the prediction of the MGT model in comparison to the other existing models (Lord–Shulman (LS) and the Green–Nagdhi theory of type III (GN-III) models) are highlighted.

Dynamic crack propagation under thermal impact

This paper addresses the dynamic crack growth in an isotropic media subjected to a non-classical thermal shock by implementing the Green-Naghdi (GN) generalized thermoelasticity theory in the eXtended Finite Element Method (XFEM). To satisfy the crack tip singularity for modeling dynamic crack growth via XFEM, proper enrichment functions for field variables are needed, which are extracted from the asymptotic fields for a dynamically growing crack in a thermoelastic media. These near tip fields of a dynamically moving crack are also used in the formulations of the maximum circumferential stress criterion and the equivalent stress intensity factor. Finally, numerical examples of the dynamic crack propagation under thermal shock are given out, and the effect of the dissipation coefficient in the GN model and the thermal shock amplitude on the crack growth path is studied in detail. In addition, the crack propagation under GN thermal shock is compared with that under classic thermal shock. The main difference between them is discussed in a numerical example.

Thermal Conductivity Study of an Orthotropic Medium Containing a Cylindrical Cavity

An interesting feature that appears in the thermoelastic interaction in an orthotropic material containing cylindrical cavities is addressed in this study. For this purpose, the Finite Element Method is applied to analyze a generalized thermoelasticity theory with a relaxation time. For the development of the model, a thermal conductivity that is dependent on the temperature of the orthotropic medium was considered. The boundary condition for the internal surface of a cylindrical hollow is defined by the thermal shocks and the traction on the free surface. The nonlinear formulations of thermoelastic based on thermal relaxation time in orthotropic mediums are abbreviated using the Finite Element Method. The nonlinear equations without Kirchhoff’s transformations are presented. The results are graphically represented to demonstrate how changing thermal conductivity affects all physical values.

Thermoelastic damping in circular microplate resonators based on fractional dual-phase-lag model and couple stress theory

In the present work, thermoelastic damping in a micro-resonator operating in vacuum as a vibrating size-dependent circular thin plate is studied. To better describe the heat conduction process, a generalized thermoelasticity theory of fractional dual-phase-lag (DPL) incorporating the couple stress theory is put forward to capture the experimentally observed small-scale effect of thermoelastic dissipation. The complex frequency of the micro-plate is obtained through Laplace transform technique. Finally, Lifshitz and Roukes’s complex frequency method is employed to derive an analytical expression for thermoelastic damping. The influences of the parameters including fractional order, phase-lag time, and internal characteristic length on the inverse quality factor Q−1 are analyzed. The obtained results show that the influences of these parameters on thermoelastic damping are pronounced. These results are helpful to the design of micro-/nano-resonators with high-performance.

Waves propagation for magneto-thermoelastic medium during the two-temperature theory with the gravitational field

The interaction between the generalized thermoelasticity theory and two-temperature theory is studied in the context of the two-dimensional (2D) deformation processes of an elastic medium. The influences of the gravitational field, hydrostatic initial stress, and magnetic field are used during the problem discretion in the context of the Lord-Şhulman (L-S) theory, the Green-Naghdi theory of type III (G-N III), and the three-phase-lag model (3PHL). The general solutions are obtained when the interaction between different fields (gravity field and magnetic field) occurs. The harmonic vibration technique in the physical domain is used to obtain the main exact expressions (physical quantities) for the waves’ velocity and attenuation coefficients for (i) Stoneley waves, (ii) Love waves, and (iii) Rayleigh waves. Different types of boundary conditions, according to the heating processes, are taken into account. Comparisons are carried out according to the effect of relaxation times (three theories of thermoelasticity). The obtained results are calculated numerically and presented graphically with some comparisons in the absence and the presence of the gravity field, the hydrostatic initial stress, and the magnetic field.

Generalized thermoelastic in a fiber-reinforced medium with cylindrical cavity under G-N theory

The present paper is aimed at studying the wave propagation for a problem of cylindrical cavity. The material is assumed to be fiber-reinforced with increased stiffness, strength and load bearing capacity. Using generalized thermoelasticity theory, Green and Nagdhi, with and without energy dissipation. Laplace transform techniques are used to derive the solution in the Laplace transform domain. The inversion process is carried out using a numerical method based on Fourier series expansions. The results obtained are displayed by graphs to clear the phenomena physical meaning and compeer with generalized thermoelasticity theories.

Analysis of size effects on thermoelastic damping in the Kirchhoff’s plate resonator under Moore–Gibson–Thompson thermoelasticity

Nanoresonators with ultra-high resonant frequency have found useful applications as electromechanical systems in today’s time. This current work presents an analytical technique for measuring thermoelastic damping (TED) and dynamic behavior of micro/nano Kirchhoff plate resonators using Moore–Gibson–Thompson (MGT) generalized thermoelasticity theory. Modified couple stress theory (MCST) is employed here to take into account the size effect for micro/nano plate. This work comprehensively evaluated the frequency shift and normalized attenuation in the micro plate resonator in the frame of the recently introduced MGT thermoelasticity theory to obtain the closed-form analytical expression for quality factor (QF). The outcomes are compared with the corresponding results of classical continuum theory and classical thermoelasticity theory. Finally, the influence of various parameters including size effects on TED in micro plate resonators has been investigated by carrying out the numerical computation of the present analytical results for different materials. Several important points are highlighted.

Moore-Gibson-Thompson theory of a non-local excited semiconductor medium with stability studies

The present study introduces a theoretical framework according to the Moore-Gibson-Thompson (MGT) Model in the context of generalized thermoelasticity theory. The excited semiconductor material is utilized to formulate the governing equations in one dimensional (1D) with a non-local parameter. According to the photo- thermoelasticity theory, the overlapping between the electronic (optical) deformation and elastic deformation is taken into account. During the photo-excitation processes, the non-local equation of motion and the heat equation is introduced according to the model of Moore-Gibson-Thompson (MGT). The novel model describes the interaction between plasma and thermomechanical waves in a non-dimensional form. Laplace transform for time variable is applied to convert the governing equations into system of ordinary differential equations. The vector-matrix differential equation with the eigenvalues approach method is employed to obtain the solutions of the physical quantities analytically. Laplace transform invers numerically is utilized when some boundary conditions are applied at the semiconductor free surface to obtain the complete general of the main physical quantities. The numerical computations for the input parameters of Silicon as semiconductor material are used to illustrate the obtained results graphically and discussed.